.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
|
i2 : M = R^4
4
o2 = R
o2 : R-module, free
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i3 : A = random(M,M)
o3 = | -44 -46 43 39 |
| -21 14 -28 23 |
| 0 22 48 -5 |
| -18 -20 -34 -17 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
2
o4 = (x + 22)(x + 34)(x + 44x + 17)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 30 -12 -39 31 |, | -37 30 50 19 |)
| 0 1 0 0 | | 3 38 29 -48 | | -14 28 41 19 |
| 0 0 -44 1 | | -22 50 -27 12 | | -42 -9 -39 1 |
| 0 0 -17 0 | | 47 48 14 44 | | -3 -23 -49 0 |
o5 : Sequence
|
i6 : B - P*A*Q == 0
o6 = true
|
i7 : P*Q - id_M == 0
o7 = false
|